Gujarat Board GSEB Textbook Solutions Class 11 Maths Chapter 1 Sets Ex 1.1 Textbook Questions and Answers.

## Gujarat Board Textbook Solutions Class 11 Maths Chapter 1 Sets Ex 1.1

Question 1.

Which of the following are sets? Justify your answer?

- The collection of all months of a year beginning with letter J.
- The collection of ten most talented writers of India, (iit) A team of eleven best cricket batsmen of the world.
- The collection of all boys in your class.
- The collection of all natural numbers less than 100.
- The collection of all natural numbers less than 100.
- A collection of novels written by the writer Munshi Prem Chand.
- The collection of all even integers.
- The collection of questions in this chapter.
- A collection of most dangerous animals of the world.

Solution:

1. We can definitely say that the members of this collection are:

January, June, July.

So, this collection is well-defined and hence, it is a set.

2. The term ‘most talented’ is a vague term. A writer may be most talented to one person and may not be so to the other.

Thus, we cannot judge definitely which writers are there in our collection.

∴ This collection is not well-defined and hence, it is not a set.

3. The term ‘best’ is a vague term. A batsmen may be best to one person and may not be so to the other.

Thus, we cannot judge definitely which batsmen are there in our collection.

∴ This collection is not well-defined and hence, it is not a set.

4. We will definitely say that the members of this collection are your classfellows.

∴ This collection is well-defined and hence, it is a set.

5. Clearly, the members of collection are 1,2, 3, …, 97, 98, 99.

∴ This collection is well-defined and hence, it is a set.

6. Clearly, the members of collection are the novels written by Munshi Prem Chand.

∴ This collection is well-defined and hence, it is a set.

7. We can definitely say that the members of this collection are 2, 4, 6,

∴ This collection is well-defined and hence, it is a set.

8. Clearly, the members of the collection are the different questions of this chapter.

So, it is well-defined and hence, it is a set.

9. The term ‘most dangerous’ is a vague term. An animal may be most dangerous to one person and may not be so to the other. So, it is not a set.

Question 2.

Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank spaces.

- 5 …………………. A
- 8 …………………….. A
- 0 ………………………. A
- 4 …………………….. A
- 2 ………………………… A
- 10 ……………………………. A

Solution:

- 5 ∈ A
- 8 ∉ A
- 4 ∉ A
- 4 ∈ A
- 2 ∈ A
- 10 ∉ A

Question 3.

Write the following sets in the roster form:

- A = [x : x is an integer and – 3 ≤ x < 7}
- B = {x : x is a natural number less than 6}
- G = {x : x is a two digit natural number such that sum of its digits is 8}
- D = {x : x is a prime number which is a divisor of 60}
- E = the set of all letters in the word TRIGONOMETRY.
- F = the set of all letters in the word BETTER.

Solution:

- A = {- 3, – 2, – 1, 0, 1, 2, 3, 4, 5, 6}
- B = {1, 2, 3, 4, 5}
- C = {17, 26, 36, 44, 63, 62, 71, 80}
- D = {2, 3, 5}
- E = {T, R, I, G, O, N, M, E, Y}
- F = {B, E, T, R}

Question 4.

Write the following sets in the set builder form:

- {3, 6, 9, 12}
- {2, 4, 8, 16, 32}
- {5, 25, 125, 625}
- {2, 4, 6, …}
- {1, 4, 9, … , 100}

Solution:

- A = [x : x is a natural number multiple of 3 and x < 15}
- B = {x : x = 2
^{n}, n ∈ N and n ≤ 6} - C = {x : x = 5
^{n}, and n ∈ N and n ≤ 4} - D = {2 : x is an even natural number}
- E = {x : x = n
^{2}, n ∈ N and n < 11}

Question 5.

List all the elements of the following sets:

- A = {x : x is an odd natural number}
- B = {x : x is an integer, – \(\frac{1}{2}\) < x < \(\frac{9}{2}\)}
- C = {x : x is an integer, x
^{2}≤ 4} - D = (x : x is a letter in the word “LOYAL”}
- E = {x : x is a month of a year not having 31 days}
- F = {x : x is a consonant in the English alphabet which precedes k).

Solution:

- A = (1, 3, 5, 7, …}
- B = {0, 1, 2, 3, 4}
- C = {- 2, – 1, 0, 1, 2}
- D = {L, O, Y, A}
- E = {February, April, June, September, November}
- F = [b, c, d, f, g, h, j}.

Question 6.

Match each of the sets on the left in the roster form with the same set on the right described in the set builder form:

(i) {1, 2, 3, 6}

(a) {x : x is a prime number and a divisor of 6}

(ii) {2, 3}

(b) {x : x is an odd natural number less than 10}

(iii) {M, A, T, H, E, I, C, S}

(c) {x : x is a natural number and divisor of 6}

(iv) {1, 3, 5, 7, 9}

(d) (x : x is a letter of the word MATHEMATICS}

Solution:

(i) ⟷ (c)

(ii) ⟷ (a)

(iii) ⟷ (d)

(iv) ⟷ (b)